Is there a way to change the sticky post to the normal white background
a) for this certain post or
b) generally for my blog (preferred).

If you post some code, please explain clearly where to paste it:
- in the concerned post, in HTML view, on top (and is there something else to be posted at the post's bottom?)
- somewhere else in the dashboard?

I tried to paste some of the code mentioned in this thread (incl. the last code mentioned by Sacred Path) to the top of my specific sticky post, but it didn't help (the code appeared visible on the page, the background remained unwantedly blue).

If it is not possible, are there other comparable no-fuss themes where the sticky post does not stick out? (Changing the header photo's size is no problem for me).

Yes, but that's not correct. It doesn't make sense to have all those values added to the property when at the end you'll just tell the browser the element doesn't have a background. It's like writing something like this: